Theory of Sobolev Multipliers With Applications to Differential and Integral Operators /

The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results. Part...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Maz'ya, Vladimir G. (Συγγραφέας), Shaposhnikova, Tatyana O. (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
Σειρά:Grundlehren der mathematischen Wissenschaften, 337
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Maz'ya, Vladimir G.  |e author. 
245 1 0 |a Theory of Sobolev Multipliers  |h [electronic resource] :  |b With Applications to Differential and Integral Operators /  |c by Vladimir G. Maz'ya, Tatyana O. Shaposhnikova. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg,  |c 2009. 
300 |a XIV, 614 p. 2 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Grundlehren der mathematischen Wissenschaften,  |x 0072-7830 ;  |v 337 
505 0 |a Description and Properties of Multipliers -- Trace Inequalities for Functions in Sobolev Spaces -- Multipliers in Pairs of Sobolev Spaces -- Multipliers in Pairs of Potential Spaces -- The Space M(B m p ? B l p ) with p > 1 -- The Space M(B m 1 ? B l 1) -- Maximal Algebras in Spaces of Multipliers -- Essential Norm and Compactness of Multipliers -- Traces and Extensions of Multipliers -- Sobolev Multipliers in a Domain, Multiplier Mappings and Manifolds -- Applications of Multipliers to Differential and Integral Operators -- Differential Operators in Pairs of Sobolev Spaces -- Schrödinger Operator and M(w 1 2 ? w ?1 2) -- Relativistic Schrödinger Operator and M(W ½ 2 ? W ?½ 2) -- Multipliers as Solutions to Elliptic Equations -- Regularity of the Boundary in L p -Theory of Elliptic Boundary Value Problems -- Multipliers in the Classical Layer Potential Theory for Lipschitz Domains -- Applications of Multipliers to the Theory of Integral Operators. 
520 |a The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results. Part I is devoted to the theory of multipliers and encloses the following topics: trace inequalities, analytic characterization of multipliers, relations between spaces of Sobolev multipliers and other function spaces, maximal subalgebras of multiplier spaces, traces and extensions of multipliers, essential norm and compactness of multipliers, and miscellaneous properties of multipliers. Part II concerns several applications of this theory: continuity and compactness of differential operators in pairs of Sobolev spaces, multipliers as solutions to linear and quasilinear elliptic equations, higher regularity in the single and double layer potential theory for Lipschitz domains, regularity of the boundary in $L_p$-theory of elliptic boundary value problems, and singular integral operators in Sobolev spaces. 
650 0 |a Mathematics. 
650 0 |a Mathematical analysis. 
650 0 |a Analysis (Mathematics). 
650 0 |a Functional analysis. 
650 0 |a Integral equations. 
650 0 |a Partial differential equations. 
650 1 4 |a Mathematics. 
650 2 4 |a Analysis. 
650 2 4 |a Integral Equations. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Functional Analysis. 
700 1 |a Shaposhnikova, Tatyana O.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783540694908 
830 0 |a Grundlehren der mathematischen Wissenschaften,  |x 0072-7830 ;  |v 337 
856 4 0 |u http://dx.doi.org/10.1007/978-3-540-69492-2  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)